J Comput Neurosci (2008) 24:113–136 DOI 10.1007/s10827-007-0044-8 Spike-frequency adaptation generates intensity invariance in a primary auditory interneuron Jan Benda · R. Matthias Hennig Received: 4 October 2005 / Revised: 27 April 2007 / Accepted: 30 April 2007 / Published online: 30 May 2007 © Springer Science + Business Media, LLC 2007 Abstract Adaptation of the spike-frequency response to constant stimulation, as observed on various timescales in many neurons, reflects high-pass filter properties of a neuron’s transfer function. Adaptation in general, however, is not sufficient to make a neu- ron’s response independent of the mean intensity of a sensory stimulus, since low frequency components of the stimulus are still transmitted, although with reduced gain. We here show, based on an analytically tractable model, that the response of a neuron is intensity invari- ant, if the fully adapted steady-state spike-frequency response to constant stimuli is independent of stimu- lus intensity. Electrophysiological recordings from the AN1, a primary auditory interneuron of crickets, show that for intensities above 60 dB SPL (sound pressure level) the AN1 adapted with a time-constant of ∼ 40 ms to a steady-state firing rate of ∼ 100 Hz. Using identical random amplitude-modulation stimuli we verified that the AN1’s spike-frequency response is indeed invariant to the stimulus’ mean intensity above 60 dB SPL. The transfer function of the AN1 is a band pass, resulting from a high-pass filter (cutoff frequency at 4 Hz) due Action Editor: Israel Nelken J. Benda (B ) Institute for Theoretical Biology, Biology Department, Humboldt University, Invalidenstr. 43, 10115 Berlin, Germany e-mail: j.benda@biologie.hu-berlin.de R. Matthias Hennig Behavioral Physiology, Biology Department, Humboldt University, Invalidenstr. 43, 10115 Berlin, Germany to adaptation and a low-pass filter (100 Hz) determined by the steady-state spike frequency. Thus, fast spike- frequency adaptation can generate intensity invariance already at the first level of neural processing. Keywords Spike-frequency adaptation · Invariance · Model · Auditory system · Cricket 1 Introduction Spike-frequency adaptation, a relaxation of an initially high spike-frequency to a lower steady-state level in response to a constant stimulus, is a common prop- erty of many neurons (Sobel and Tank 1994; Wang 1998; Sanchez-Vives et al. 2000; Fuhrmann et al. 2002; Gabbiani and Krapp 2006). The slow adaptation dy- namics often acts subtractively on the input to the neuron, independent of the details of the underlying adaptation mechanism (Benda and Herz 2003). Sub- tractive adaptation adds a high-pass filter to the neu- ron’s transfer function (Nelson et al. 1997; French et al. 2001; Benda et al. 2005). A high-pass filter attenuates slow stimulus components including the mean, whereas fast stimulus components are transmitted with high gain. Fast and slow stimulus components are distin- guished by the cutoff frequency that is determined by the neuron’s adaptation time-constant (Benda et al. 2005). If the slow stimulus components were suppressed completely, then the response to fast components will be independent of the mean intensity of the stimulus. Consequently, the response of such a neuron will be intensity invariant.